While quantum many-body models are generally insoluble except in very special cases, by extending the global symmetry of the model from \(\textsf {SU}(2)\)  to a larger group such as \(\textsf {SU}(N)\)  or \(\textsf {Sp}(N)\) , a systematic expansion in powers of \(1/N\)  about the \(N\rightarrow \infty \)  limit can often be derived [1]}, [2]}, [3]}, [4]}, [5]}, [6]}.
Here, we present a large-\(N\)  generalization of the Hubbard model that allows controlled access to a variety of intermediate-coupling spin and charge ordered phases. Consider the Hamiltonian
\(H=-\sum _{\langle ij\rangle }\sum _{\alpha =\pm }\sum _{m=1}^N c^\dagger _{i\alpha m}\big (t^{\vphantom{\dagger }}_{ij} + \mu \,\delta ^{\vphantom{\dagger }}_{ij}\big ) c^{\vphantom{\dagger }}_{j\alpha m} + {1\over N} \sum _i \big ({\textstyle {1 \over 2}}V n^2_i - {\textstyle {1 \over 2}}J\mathbf {S}^{\,2}_i + {\textstyle {1 \over 2}}K {\rm \Psi }^\dagger _i{\rm \Psi }^{\vphantom{\dagger }}_i\big )\quad ,\) 
